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Physical Review A

Universal criteria for entanglement-assisted dynamical speed enhancement

Yusef Maleki, Muhammad Suhail Zubairy

Published Nov 12, 2024• 4 citations
Publisher

Abstract

Quantum speed limits, establishing fundamental thresholds for the speed of quantum processes, are central to a wide spectrum of applications of quantum science, ranging from speeding up gate operations in quantum computations and optimizing communication channels to unraveling the rate at which correlations can propagate within many-body systems. In the quest to tailor optimal quantum dynamical speeds, the role of quantum entanglement has been showcased in specific instances. However, a robust universal link between system entanglement and its dynamical speed remains elusive. Here, we formulate the genuine contribution of quantum entanglement by developing universal criteria determining this speed enhancement within a quantum system. Specifically, we establish an upper limit that rigorously bounds the speed of the dynamical evolution of separable states, providing an unattainable speed threshold for these states. Our findings underscore the capacity of quantum entanglement to surpass this limit, demonstrating its capability as a resource for enhancing dynamical speed of the system.

DOI
10.1103/physreva.110.052415

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Quantum speed limits, establishing fundamental thresholds for the speed of quantum processes, are central to a wide spectrum of applications of quantum science, ranging from speeding up gate operations in quantum computations and optimizing communication channels to unraveling the rate at which correlations can propagate within many-body systems. In the quest to tailor optimal quantum dynamical speeds, the role of quantum entanglement has been showcased in specific instances. However, a robust universal link between system entanglement and its dynamical speed remains elusive. Here, we formulate the genuine contribution of quantum entanglement by developing universal criteria determining this speed enhancement within a quantum system. Specifically, we establish an upper limit that rigorously bounds the speed of the dynamical evolution of separable states, providing an unattainable speed threshold for these states. Our findings underscore the capacity of quantum entanglement to surpass this limit, demonstrating its capability as a resource for enhancing dynamical speed of the system.
Research in quantum information science aims to surpass the scaling limitations of classical information processing. From a physicist's perspective, performance improvement involves a physical speedup in the quantum domain, achieved by dynamically exploiting quantum correlations. In this study, speed limits in interacting quantum systems are derived by comparing the rates of change in actual quantum dynamics with the quasiclassical evolution confined to the manifold of nonentangled separable states. The utility of the resulting bounds on entanglement-assisted speedup is demonstrated on bipartite qubit systems, bipartite qudit systems, as well as a complex multimode systems. Specifically, the proposed speed limits provide a tight bound on quantum speed advantage, including a quantum gain that can scale exponentially with the system's size. Extensions of the results to open systems and measurable witnesses are discussed.
The speed limit on entanglement is defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and trace-distance entanglement, for unitary and arbitrary quantum dynamics, where we assume that the dynamics of the closest separable state can be approximately described by the closest separable dynamics of the actual dynamics of the system. For the unitary dynamics of isolated bipartite systems which are described by pure states, the rate of entanglement production is bounded by the product of fluctuations of the system's driving Hamiltonian and the surprisal operator, with an additional term reflecting the time-dependent nature of the closest separable state. Removing restrictions on the purity of the input and on the unitarity of the evolution, the two terms in the bound get suitably altered. Furthermore, we find a lower bound on the time required to generate or degrade a certain amount of entanglement by arbitrary quantum dynamics. We demonstrate the tightness of our speed limits on entanglement by considering quantum processes of practical interest.
Entanglement is closely related to some fundamental features of the dynamics of composite quantum systems: quantum entanglement enhances the "speed" of evolution of certain quantum states, as measured by the time required to reach an orthogonal state. The concept of "speed" of quantum evolution constitutes an important ingredient in any attempt to determine the fundamental limits that basic physical laws impose on how fast a physical system can process or transmit information. Here we explore the relationship between entanglement and the speed of quantum evolution in the context of the quantum brachistochrone problem. Given an initial and a final state of a composite system we consider the amount of entanglement associated with the brachistochrone evolution between those states, showing that entanglement is an essential resource to achieve the alluded time-optimal quantum evolution.
The quantum speed limit provides fundamental bound on how fast a quantum system can evolve between the initial and the final states. For the unitary evolution, the celebrated Mandelstam-Tamm (MT) bound has been widely studied for various systems. Here, we prove a stronger quantum speed limit (SQSL) for all quantum systems undergoing arbitrary unitary evolution and show that the MT bound is a special case of the stronger quantum speed limit. We apply our result for single system as well as for composite systems in separable and entangled states and show that the new bound is indeed tight. The stronger quantum speed limit will have wide range of applications in quantum control, quantum computing and quantum information processing.
Quantum speed limits (QSLs) impose fundamental constraints on the evolution speed of quantum systems. For systems with time-independent Hamiltonians, the QSLs are intricately linked to the energy spectra of the initial state, which signify the generalization of the time-energy uncertainty relation. Based on arbitrary-order norms of the Hamiltonian, dual energies from inverted spectra, and the standard deviation of energy, different types of QSLs have been proposed, revealing three dynamical parameter regimes of quantum state evolution. Despite the theoretical advancements, a comprehensive experimental examination remains elusive. In this research, by introducing unified bounds suitable for all evolution times, we present the experimental verification to the QSLs in various scenarios with a superconducting circuit. We explore the dynamical evolution with regard to each parameter regime as well as the critical point by carefully engineering the initial-state population of the superconducting resonator. We test our unified bounds over finite-level states and infinite-level classical and nonclassical Gaussian states, which validates the criteria for the QSLs. Our work substantially deepens our comprehension of unitary quantum evolution.
Quantum speed limits (QSLs) provide an upper bound for the speed of evolution of quantum states in any physical process. Based on the Stratonovich-Weyl correspondence, we derive a universal QSL bound in arbitrary phase spaces that is applicable for both continuous variable systems and finite-dimensional discrete quantum systems. This QSL bound allows the determination of speed limit bounds in specific phase spaces that are tighter than those in Wigner phase space or Hilbert space under the same metric, as illustrated by several typical examples, e.g., a single-mode free field and NNN-level quantum systems in phase spaces. This QSL bound also provides an experimentally realizable way to examine the speed limit in phase spaces relevant to applications in quantum information and quantum optics.